“The number of companies that are willing to sponsor a visa is pretty limited.”

You're studying in the U.S. You'd like to find a job, but you can't because you need a working visa. Most companies won't help you to get a visa because it takes time and money. You explain why you can't find a job to one of your American friends.

The number of companies that are willing to sponsor a visa is pretty limited.

A "visa" is a document which permits you to visit or live in a foreign country.

Many countries have restrictions on who can live and work there. You might not be allowed to move there unless you meet some qualifications like being married to a citizen of that country, or having a job offer from a company which wants to hire you.

If a company wants to hire a foreigner, it must "sponsor" that person's visa application. This means that the company sends certain paperwork to the government to prove that it needs to hire this person. The company may have to spend some money on it. So a lot of companies do not sponsor foreigners' visas.

Some other things that companies "sponsor" include:

sponsor a TV show

sponsor a conference

In these cases, "sponsoring" something means giving money to support it.